A long straight wire carrying current of `30 A` is placed in an external unifrom magnetic field of induction `4xx10^(4) T`. The magnetic field is acting parallel to the direction of current. The maggnetic of the resultant magnetic inuduction in tesla at a point `2.0 cm` away form the wire is

Options

A. `10^(-4)`
B. ` 3xx10^(-4)`
C. ` 5xx10^(-4)`
D. `6xx10^(-4)`

Answer

C

Explanation

Magnetic field due to wire
`B = (mu_(0) I)/(2pi r ) = (4pi xx 10^(-7))/(2 pi) xx (30)/( 2 xx 10^(-2))`
= `3 xx 10^(-4) T`
This magnetic field will be perpendicular to external magnetic field.
`therefore` Net magnetic field
B = `sqrt(B^(2) + B_(0)^(2))`
= `sqrt((3 xx 10^(-4))^(2) + (4 xx 10^(-4))^(2))`
= `5 xx 10^(-4) T `